Chapter 4.5, Problem 3WE

To determine

To prove:In given figure, $\angle H=\angle F$ .

Explanation of Solution

Given information:In the given figure, $\overline{EF}\perp \overline{EG},\overline{HG}\perp \overline{EG},\overline{EH}\cong \overline{GF}$ .

  

Conceptused:In two right triangles, if corresponding hypotenuse and one pair of corresponding sides are congruent, then by HL congruency, both triangles are congruent and in congruent triangles, corresponding angles are always congruent.

Calculation: The two column proof:

S.No.	Statements	Reasons
1.	$\overline{EF}\perp \overline{EG}$	Given
2.	$m\angle GEF={90}^0$	Definition of perpendicular lines
3.	$\overline{HG}\perp \overline{EG}$	Given
4.	$m\angle EGH={90}^0$	Definition of perpendicular lines
5.	$\overline{EH}\cong \overline{GF}$	Given
6.	$\overline{EG}\cong \overline{EG}$	Reflexive property
7.	$\Delta EGH\cong \Delta GEF$	HL congruency
8.	$\angle H=\angle F$	CPCT

Conclusion: Thus, by above proof, it is proved that $\angle H=\angle F$ .